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Pelosi's shifting statements on John Conyers

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Pelosi has found the sexual harassment allegations against Conyers "a very difficult process" to deal with

Pelosi has a strained history with the CBC

Washington (CNN)House Minority Leader Nancy Pelosi has struggled with how to address the sexual harassment allegations against Rep. John Conyers as she balances a key black caucus' sensitivities toward one of its founders with the need to swiftly act during a time of heightened awareness about sexual misconduct.

On NBC's "Meet the Press" Sunday morning, Pelosi wouldn't say whether she believed the former Conyers staff members who have accused him of sexual harassment and workplace abuse. In the interview, she called him an "icon" who has "done a great deal to protect women," citing his support of the Violence Against Women Act.

A senior Democratic aide tells CNN that Pelosi has found the sexual harassment allegations against Conyers "a very difficult process" to deal with, in part, because he's a member of the Congressional Black Caucus.

Asked why Pelosi refused to answer the question of whether she believes the accusers on "Meet the Press," the aide said it has everything to do with the fact that the two women who have made allegations against Conyers are still unnamed.

"CBC members feel that over time, they've been unfairly targeted and they go into this scenario with raw feelings about how the process works," the aide said.

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The CBC didn't immediately return a CNN request for comment.

During the "Meet the Press" interview, Pelosi would also not say whether Conyers should be removed as the top Democrat on the House Judiciary Committee, but believed he would "do the right thing." He resigned from the committee post later that day and continues to deny the allegations. Another aide told CNN that Pelosi worked behind the scenes with Conyers and other CBC members to lay the groundwork for him to step aside gracefully.

The first aide stressed, as Pelosi suggested Sunday, that Conyers stepping down as ranking member of Judiciary Committee was the "correct outcome."

Pelosi believes she would be setting a "dangerous precedent" if "any anonymous complaint" leads to a member being declared guilty, the aide said.

The aide went as far as to say: "I think if she was asked about (Sen. Al) Franken in that way, there would be a different answer." Several women who have provided their names have revealed that Franken groped them, and he has apologized for the behavior.

Pelosi has a strained history with the CBC.

According to The Washington Post, the caucus accused Pelosi of a "racially tinged double standard" back in 2007, when she worked to oust Rep. William Jefferson, D-Louisiana, from the Ways and Means Committee -- while he was being investigated for allegedly keeping money accepted from an FBI informant stashed in a freezer -- while permitting Rep. Alan Mollohan, D-West Virginia, who is white, to stay on a committee during his federal investigation.

There were similar tensions when Pelosi opted to censure Rep. Charlie Rangel, D-New York, in 2010 for violating House rules on several counts, including failing to pay taxes on a vacation home. All but one of the CBC's members voted against censure.

And in 2014, the CBC pushed back when Pelosi planned to endorse Rep. Anna Eshoo, D-California, over a more senior member to be the next ranking member of the Energy and Commerce Committee. Since long-serving CBC members hold a number of top committee slots, the move angered many in the CBC.

"When I first came here 10 years ago, the conversation among members was, 'Seniority mattered,'" said Rep. G.K. Butterfield, D-North Carolina, who became the CBC chair the following congressional session, told Roll Call in 2014.

"As the years went on, the conversation became, 'Seniority is important, but not controlling.' Then the conversation was, 'Seniority is a factor.' And now the discussion among some is that seniority really should not be a determinant. That is not the direction I want our caucus to go," he added.